# Faraday's laws of electrolysis

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Faraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1834.[1] They relate the amount of material produced at an electrode during an electrochemical reaction to the total charge passed or, equivalently, the average current and total time.

## Mathematical form

Faraday's laws can be summarized by

${\displaystyle m={\frac {QM}{Fz}}}$

where:

• m is the mass of the substance liberated at an electrode in grams
• Q is the total electric charge passed through the substance in coulombs
• F = 96485.33289(59) C mol−1 is the Faraday constant
• M is the molar mass of the substance in grams per mol
• z is the valency number of ions of the substance (electrons transferred per ion).

Note that M/z is the same as the equivalent weight of the substance altered.

For Faraday's first law, M, F, and z are constants, so that the larger the value of Q the larger m will be.

For Faraday's second law, Q, F, and z are constants, so that the larger the value of M/z (equivalent weight) the larger m will be.

In the simple case of constant-current electrolysis, ${\displaystyle Q=It}$  leading to

${\displaystyle m={\frac {ItM}{Fz}}}$

and then to

${\displaystyle n={\frac {It}{Fz}}}$

where:

• n is the amount of substance ("number of moles") liberated: n = m/M
• t is the total time the constant current was applied.

In the more complicated case of a variable electric current, the total charge Q is the electric current I(${\displaystyle \tau }$ ) integrated over time ${\displaystyle \tau }$ :

${\displaystyle Q=\int _{0}^{t}I(\tau )d\tau }$

Here t is the total electrolysis time.[2]

## References

1. ^ Ehl, Rosemary Gene; Ihde, Aaron (1954). "Faraday's Electrochemical Laws and the Determination of Equivalent Weights". Journal of Chemical Education. 31 (May): 226–232. Bibcode:1954JChEd..31..226E. doi:10.1021/ed031p226.
2. ^ For a similar treatment, see Strong, F. C. (1961). "Faraday's Laws in One Equation". Journal of Chemical Education. 38 (2): 98. Bibcode:1961JChEd..38...98S. doi:10.1021/ed038p98.

## Further reading

• Serway, Moses, and Moyer, Modern Physics, third edition (2005), principles of physics.